The DMS for the marker is often stamped right into the head of the monument itself, and should be a couple orders of magnitude more reliable than a GPS (even taking into account seismic activity with the exception of New Madrid), particularly in cooler climates (the western US is notorious for heat induced measuring errors in 19th century surveys) and more recent decades. That said, I wouldn’t map the temporary markers pictured assuming the surveyors didn’t stake the monument just for visibility sake, but rather map the monument itself. This is especially true for monuments within the highway right of way, as many DOTs (Oklahoma, California and Oregon for sure from experience) will often paint large + markings with the monument centered in the +, handy for imagery alignment purposes.